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EnviroLink Forum • View topic - Simple v complex depends on the level of understanding

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PostPosted: Wed May 31, 2006 6:24 pm 
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Engineering Procedure
Engineering Procedure from an unknown but astute source:
Every new engineer must learn early that is it never good taste to designate the sum of two quantities in the form:

1 + 1 = 2 (1)

Anyone who has made a study of advanced mathematics is aware that:

1 = ln e

and that:

1 = sin2 x + cos2 x

further:

2 = n=0Σn=¥ (1/2n)

Therefore, Eq. (1) can be expressed more scientifically as:

ln e + (sin2 x + cos2 x) = n=0Σn=¥ (1/2n) (2)

This may be further simplified by the use of the relations:

1 = cosh y √ (1-tanh2 y)

and

e = lim z-¥ (I + 1/z)z

Equation (2) may therefore be rewritten:

ln [lim z-¥ (I + 1/z)z] + (sin2 x + cos2 x) = n=0Σn=¥ (cosh y √ (1-tanh2 y)/ 2n)
(3)

At this point, it should be obvious that Eq, (3) is much clearer and more easily understood than Eq. (1). They are the same thing!

Other methods of a similar nature could be used to clarify Eq. (1) but - these are easily discovered once the reader grasps the underlying principles.

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